Given: x ∈ Z and x² = x

Z is a set of integers

Integers are …-2 , -1, 0, 1, 2, …

Now, if we take x = -2 then we have to check that it satisfies the given condition x² = x

(-2)² = 4 ≠ 2

So, -2 ∉ E

If x = -1 then (-1)² = 1 ≠ -1 [not satisfying x² = x]

So, -1 ∉ E

If x = 0 then (0)² = 0 [satisfying x² = x]

∴ 0 ∈ E

If x = 1 then (1)² = 1 [satisfying x² = x]

∴ 1 ∈ E

If x = 2 then (2)² = 4 ≠ 2 [not satisfying x² = x]

⇒ 2 ∉ E

So, E = {0, 1}